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Re: What exactly is "exact" (was Clean Singleton Docstrings)

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Subject Re: What exactly is "exact" (was Clean Singleton Docstrings)
Date Mon, 18 Jul 2016 09:32:19 -0400
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On Mon, Jul 18, 2016, at 01:37, Rustom Mody wrote:
> The INTENTION is that in addition to capturing the usual number tower
> ℕ ⊂ ℤ ⊂ ℝ (or parts therefore)

Well, ℚ. You hardly ever see representations of numbers that are in ℝ-ℚ.

> scheme also captures ORTHOGONALLY (word in the docs) the (in)exactness
> attribute
>
> In the realization, the designers need to (over)load these different
> attributes onto numeric constants. So the ruse chosen is that fraction-
> constants by default are exact Decimal constants are inexact And one
> can override any of these by suitable a function [At least that's my
> understanding]

The other thing you're missing is that implementations are free to
choose any representation they want (such as an IEEE binary float, or a
rational of bounded denominator) for inexact numbers, no matter how they
were written, because they're not required to preserve the exact value.
The fact that an implementation *could* also use an IEEE binary float to
represent an exact rational number whose denominator happens to be power
of two is immaterial to this discussion.

It's not required to actually be "orthogonal" in the sense that you're
imagining - i.e. being able to have inexact numbers whose machine
representations are big integers, big rationals, etc. An implementation
could choose to represent *all* inexact numbers as floats.

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Thread

Clean Singleton Docstrings Rob Gaddi <rgaddi@highlandtechnology.invalid> - 2016-07-07 23:46 +0000
  Re: Clean Singleton Docstrings Steven D'Aprano <steve@pearwood.info> - 2016-07-08 12:53 +1000
  Re: Clean Singleton Docstrings Michael Selik <michael.selik@gmail.com> - 2016-07-07 23:43 -0400
    Re: Clean Singleton Docstrings Rob Gaddi <rgaddi@highlandtechnology.invalid> - 2016-07-08 16:57 +0000
      Re: Clean Singleton Docstrings Ethan Furman <ethan@stoneleaf.us> - 2016-07-08 13:00 -0700
  Re: Clean Singleton Docstrings Peter Otten <__peter__@web.de> - 2016-07-08 09:38 +0200
    Re: Clean Singleton Docstrings Steven D'Aprano <steve@pearwood.info> - 2016-07-08 19:20 +1000
      Re: Clean Singleton Docstrings Rob Gaddi <rgaddi@highlandtechnology.invalid> - 2016-07-08 16:47 +0000
    Re: Clean Singleton Docstrings Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-07-13 15:42 -0700
      Re: Clean Singleton Docstrings Peter Otten <__peter__@web.de> - 2016-07-14 01:54 +0200
        Re: Clean Singleton Docstrings Rustom Mody <rustompmody@gmail.com> - 2016-07-15 21:04 -0700
          Re: Clean Singleton Docstrings Ethan Furman <ethan@stoneleaf.us> - 2016-07-15 21:20 -0700
            Re: Clean Singleton Docstrings Rustom Mody <rustompmody@gmail.com> - 2016-07-15 22:51 -0700
            Re: Clean Singleton Docstrings Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-07-15 23:19 -0700
              Re: Clean Singleton Docstrings Chris Angelico <rosuav@gmail.com> - 2016-07-16 16:29 +1000
              Re: Clean Singleton Docstrings Random832 <random832@fastmail.com> - 2016-07-16 02:53 -0400
                Re: Clean Singleton Docstrings Steven D'Aprano <steve@pearwood.info> - 2016-07-16 18:54 +1000
                Re: Clean Singleton Docstrings Steven D'Aprano <steve@pearwood.info> - 2016-07-16 19:46 +1000
                What exactly is "exact" (was Clean Singleton Docstrings) Rustom Mody <rustompmody@gmail.com> - 2016-07-17 21:16 -0700
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Chris Angelico <rosuav@gmail.com> - 2016-07-18 14:35 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Rustom Mody <rustompmody@gmail.com> - 2016-07-17 22:37 -0700
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Chris Angelico <rosuav@gmail.com> - 2016-07-18 15:48 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Marko Rauhamaa <marko@pacujo.net> - 2016-07-18 09:21 +0300
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Random832 <random832@fastmail.com> - 2016-07-18 09:32 -0400
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Ben Finney <ben+python@benfinney.id.au> - 2016-07-18 14:46 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Rustom Mody <rustompmody@gmail.com> - 2016-07-17 22:22 -0700
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2016-07-18 19:29 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Marko Rauhamaa <marko@pacujo.net> - 2016-07-18 13:00 +0300
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Chris Angelico <rosuav@gmail.com> - 2016-07-18 20:15 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Rustom Mody <rustompmody@gmail.com> - 2016-07-18 03:24 -0700
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Chris Angelico <rosuav@gmail.com> - 2016-07-18 20:37 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Marko Rauhamaa <marko@pacujo.net> - 2016-07-18 14:38 +0300
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Peter Otten <__peter__@web.de> - 2016-07-18 14:58 +0200
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Steven D'Aprano <steve@pearwood.info> - 2016-07-19 13:42 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Rustom Mody <rustompmody@gmail.com> - 2016-07-18 21:58 -0700
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Chris Angelico <rosuav@gmail.com> - 2016-07-19 15:30 +1000
                Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2016-07-20 15:42 +1000
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Chris Angelico <rosuav@gmail.com> - 2016-07-20 16:11 +1000
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2016-07-20 09:09 +0200
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Marko Rauhamaa <marko@pacujo.net> - 2016-07-20 10:25 +0300
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Steven D'Aprano <steve@pearwood.info> - 2016-07-20 22:47 +1000
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Marko Rauhamaa <marko@pacujo.net> - 2016-07-20 16:54 +0300
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Chris Angelico <rosuav@gmail.com> - 2016-07-21 00:26 +1000
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Marko Rauhamaa <marko@pacujo.net> - 2016-07-20 17:59 +0300
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Rustom Mody <rustompmody@gmail.com> - 2016-07-20 22:38 -0700
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Marko Rauhamaa <marko@pacujo.net> - 2016-07-21 10:52 +0300
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Chris Angelico <rosuav@gmail.com> - 2016-07-21 18:46 +1000
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Marko Rauhamaa <marko@pacujo.net> - 2016-07-21 12:09 +0300
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-07-22 00:54 +0100
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Chris Kaynor <ckaynor@zindagigames.com> - 2016-07-21 17:43 -0700
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-07-22 17:14 +0100
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Rustom Mody <rustompmody@gmail.com> - 2016-07-20 22:28 -0700
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Chris Angelico <rosuav@gmail.com> - 2016-07-21 15:35 +1000
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Rustom Mody <rustompmody@gmail.com> - 2016-07-20 22:52 -0700
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2016-07-21 16:34 +1000
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Rustom Mody <rustompmody@gmail.com> - 2016-07-21 06:14 -0700
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Steven D'Aprano <steve@pearwood.info> - 2016-07-22 02:10 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Chris Angelico <rosuav@gmail.com> - 2016-07-19 15:27 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Rustom Mody <rustompmody@gmail.com> - 2016-07-18 03:14 -0700
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Ian Kelly <ian.g.kelly@gmail.com> - 2016-07-18 09:25 -0600
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Marko Rauhamaa <marko@pacujo.net> - 2016-07-18 18:40 +0300
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Marko Rauhamaa <marko@pacujo.net> - 2016-07-18 18:55 +0300
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Ian Kelly <ian.g.kelly@gmail.com> - 2016-07-18 11:13 -0600
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Marko Rauhamaa <marko@pacujo.net> - 2016-07-18 21:58 +0300
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Rustom Mody <rustompmody@gmail.com> - 2016-07-18 17:36 -0700
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Steven D'Aprano <steve@pearwood.info> - 2016-07-19 13:16 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Rustom Mody <rustompmody@gmail.com> - 2016-07-18 20:26 -0700
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Gene Heskett <gheskett@shentel.net> - 2016-07-19 01:22 -0400
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-07-19 10:46 -0700
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Gene Heskett <gheskett@shentel.net> - 2016-07-19 16:35 -0400
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Marko Rauhamaa <marko@pacujo.net> - 2016-07-20 01:17 +0300
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Random832 <random832@fastmail.com> - 2016-07-19 23:15 -0400
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Marko Rauhamaa <marko@pacujo.net> - 2016-07-20 10:16 +0300
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Random832 <random832@fastmail.com> - 2016-07-20 10:00 -0400
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2016-07-21 10:46 +1200
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Ian Kelly <ian.g.kelly@gmail.com> - 2016-07-19 16:27 -0600
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Marko Rauhamaa <marko@pacujo.net> - 2016-07-20 02:09 +0300
                Re: What exactly is "exact" (was Clean Singleton Docstrings) alister <alister.ware@ntlworld.com> - 2016-07-20 13:24 +0000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Steven D'Aprano <steve@pearwood.info> - 2016-07-21 14:04 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-07-19 17:01 -0700
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2016-07-20 11:07 +1200
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Marko Rauhamaa <marko@pacujo.net> - 2016-07-20 02:20 +0300
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Steven D'Aprano <steve@pearwood.info> - 2016-07-19 13:03 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Random832 <random832@fastmail.com> - 2016-07-18 09:25 -0400
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Steven D'Aprano <steve@pearwood.info> - 2016-07-19 13:21 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Ben Finney <ben+python@benfinney.id.au> - 2016-07-19 10:21 +1000
              Re: Clean Singleton Docstrings Chris Angelico <rosuav@gmail.com> - 2016-07-16 17:27 +1000
                Re: Clean Singleton Docstrings Marko Rauhamaa <marko@pacujo.net> - 2016-07-16 10:58 +0300
              Re: Clean Singleton Docstrings Random832 <random832@fastmail.com> - 2016-07-16 14:04 -0400
                Re: Clean Singleton Docstrings Marko Rauhamaa <marko@pacujo.net> - 2016-07-16 21:43 +0300
              Re: Clean Singleton Docstrings Chris Angelico <rosuav@gmail.com> - 2016-07-17 07:02 +1000
                Re: Clean Singleton Docstrings Marko Rauhamaa <marko@pacujo.net> - 2016-07-17 00:27 +0300
                Re: Clean Singleton Docstrings Chris Angelico <rosuav@gmail.com> - 2016-07-17 08:18 +1000
                Re: Clean Singleton Docstrings Marko Rauhamaa <marko@pacujo.net> - 2016-07-17 10:41 +0300
                Re: Clean Singleton Docstrings Chris Angelico <rosuav@gmail.com> - 2016-07-17 17:51 +1000
                Re: Clean Singleton Docstrings Random832 <random832@fastmail.com> - 2016-07-17 04:03 -0400
                Re: Clean Singleton Docstrings Steven D'Aprano <steve@pearwood.info> - 2016-07-17 20:35 +1000
                Re: Clean Singleton Docstrings Random832 <random832@fastmail.com> - 2016-07-17 04:08 -0400
                Re: Clean Singleton Docstrings Chris Angelico <rosuav@gmail.com> - 2016-07-17 18:44 +1000
      Re: Clean Singleton Docstrings Ian Kelly <ian.g.kelly@gmail.com> - 2016-07-13 18:25 -0600
  Re: Clean Singleton Docstrings Peter Otten <__peter__@web.de> - 2016-07-08 09:44 +0200
    Re: Clean Singleton Docstrings Rustom Mody <rustompmody@gmail.com> - 2016-07-08 01:53 -0700
  Re: What exactly is "exact" (was Clean Singleton Docstrings) Gene Heskett <gheskett@shentel.net> - 2016-07-19 23:16 -0400

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